I dont think the question stem has all the information.

Consider m = 1 and n = -1 , in which case m ^ n = 1

For any other values of m and n, m ^ n will always be less than 1, but we still need to rule out the possibility of m = 1 and n = -1.

So..lets see

1) m>1 SUFF
2) n<-1 INSUFF
1/2^-5 = 2^5 = 32
and 2^-5 = 1/32

A right?

ov25 wrote:So..lets see

1) m>1 SUFF
2) n<-1 INSUFF
1/2^-5 = 2^5 = 32
and 2^-5 = 1/32

A right?

I think the answer is right, but there is a flaw in your argument.

m cannot be 1/2, since m and n are both integers.

Statement 2 tells us that n is not equal to -1, but it doesnt say anything about m. If m is 1, then n could be anything and the result would be 1, which makes statement 2 insufficient. However, statement 1 says that m is greater than 1, so for any value of n, m ^ n will always be less than 1.